When linearly polarized light (sometimes referred to as plane polarized light) is directed through an optically active crystal that exhibits double refraction, such crystal divides the incoming light into an ordinary ray and an extraordinary ray, which are vibrating in relatively orthogonal planes. Moreover, such optically active crystal tends to retard one of the rays relative to the other as they travel through the crystal thereby causing a phase difference between the two waves. The phase difference is a function of the thickness of the optically active crystal and of the wavelength of the light.
As is known, the general condition for polarized light is that of elliptical polarization. Linear polarization and circular polarization are special cases of elliptical polarization. For example, when linearly polarized light is directed through an optically active crystal that exhibits double refraction such that the axis of polarization and the axis of the crystal are at 45 degrees relative to each other and the thickness of the crystal is such that it retards one of the ordinary ray and extraordinary ray by an odd whole number multiple of 90 degrees (e.g., pi/2, 3pi/2, 5pi/2, etc.) relative to the other wave, for a particular wavelength of light, the output from the crystal will be circularly polarized light. To have circularly polarized light, the amplitude Ao of the ordinary ray and the amplitude Ae of the extraordinary ray must be equal and they must be out of phase by 90 degrees (or the mentioned odd whole number multiple thereof). This is the reason for the 45 degrees relation. In such case, the amplitudes Ao, Ae are defined, respectively, by A(sin .theta.) and A(cos .theta.), where A is the amplitude of the incident linearly polarized light to the crystal and .theta. (theta) is the angle of the vibrational plane of the electric vector of such incident light with respect to the optical axis of the crystal. When .theta. (theta) is 45 degrees, the sine and cosine functions mentioned are equal at 1, and the amplitudes, therefore, are equal.
However, if the amplitudes Ao and Ae mentioned above are not equal, whereby either the input angle .theta. (theta) is not 45 degrees and/or the retardation effected by the optically active crystal is not 90 degrees (or an odd whole number multiple thereof), then the more general case of elliptically polarized light occurs. As was mentioned above, the retardation effected by optically active crystal is a function of wavelength of the incident light.
The relationships of certain optical components for affecting light, particularly polarized light, is described, for example, in Jenkins and White FUNDAMENTALS OF OPTICS, McGraw-Hill Book Company, New York, 1957. For example, at Chapter 27 of such text, the interference of polarized light is described. Polarized light and use of various optical components with polarized light also are described elsewhere in such text. The entire disclosure of such text is incorporated herein by reference.
A liquid crystal device for phase modulating polarized light is disclosed in U.S. Pat. Nos. 4,385,806 4,436,376, 4,540,243, and U.S. Pat. No. Re. 32,521. The disclosures of such patents hereby are incorporated by reference. In such device linearly polarized light is phase-modulated as such light passes through a liquid crystal cell to which a modulated electrical carrier wave signal are applied as an electrical potential to develop an electric field across the liquid crystal material affecting alignment of the liquid crystal structure therein. The light which is transmitted through the liquid crystal cell is phase modulated as a function of the modulated electrical carrier wave signal. More specifically, the liquid crystal cell effectively separates the incident linearly polarized light into the quadrature components, i.e., the ordinary and extraordinary rays, thereof, and effects a retardation of one ray or component relative to the other as the light is transmitted through the cell. The amount of retardation, i.e., the effective optical thickness of the liquid crystal cell, is a function of the modulated electrical carrier wave signal. The liquid crystal cell disclosed in such patents utilizes a so-called surface mode switching technique which is fast acting, e.g., for example providing switching response times of as little to 10 to 100 microseconds.